Independent Component Analysis features of Color & Stereo images Authors: Patrik O. Hoyer Aapo Hyvarinen CIS 526: Neural Computation Presented by: Ajay Kumar Yadav

Overview  Introduction  Background Study  Data Preprocessing  Color Image Experiment  Stereo Image Experiment  Conclusion

Introduction  Visual Cortex: part of the cerebral cortex responsible for processing visual stimuli. (Static, Moving & Pattern Recognition)  Receptive fields are divided as: Sub-regions that exert an excitatory influence. (light grey) Sub-regions that exert an inhibitory influence. (dark grey)  Stimulus Influence also depends on size, orientation and position (Hubel & Wiesel’s -1962, DeValois-1982, DeAngelis-1993)

Contd..  Cones consist of three cell each responsible for each RGB component. (tuned at wavelength of 430, 535, 590 nanometer)  The degree to which the images are non-corresponding is defined as binocular disparity. It is used to determine the distance of an object from oneself, and its relation to the fixation plane, is called stereopsis.

Background Study  The sparseness-maximization network and ICA are closely related. (Olshausen and Field 1997)  Hateren and Vander Schaaf qualitatively compared the filter learned by ICA to measurements of neural receptive fields.  Van Hateren and Ruderman proved ICA also fit the receptive field properties for video images.

Data Preprocessing  ICA preprocess the data in two steps: The mean of the data is subtracted to center the data on the origin. Whiten the data z = Vx, so that  Goal: ICA transform W to minimize the statistical dependencies between the estimated sources.  After convergence

Color Image Experiment  Standard RGB values are considered as input data assuming the transformation to cone outputs to be roughly linear.  A total of 50, by 12 pixel image patches were sampled randomly with dimensionality of 432.  Data is preprocessed and correlation matrix and eigen vectors are calculated.  Constant RGB value is used in the display.

Correlation matrix  Data is projected in 160 principle component before whitening. Two reasons are: To emulate the real neuron functionality Dimension is dropped to lower computational cost.

Results **ICA basis of color images** **Color content of three ICA filters****Percentage of achromatic**

Stereo Image Experiment  Stereo image data: 5 focus points at random from each image are selected and estimated the disparities. Randomly sampled 16*16 pixel corresponding image in patch area of 300*300 pixels centered on each focus point. Due to the fluctuation patches are often similar but horizontally shifted.  During the preprocessing local mean was removed from each component and correlation matrix and eigenvalue decomposition are calculated.

Stereo Images **PCA Basis of Stereo Image****ICA Basis of Stereo Image** Equal Response Varying Response

Ocular Dominance  The shift from one eye to the other takes place over a distance of less than 50 microns, therefore column dominated by one eye.  If the sampling areas is smaller, correlation between the patches would be higher.  If the area gets larger, the dependencies between the left and right patches get weaker

Disparity Tuning Analysis  To analyze the disparity tuning several ICA basis were estimated using different number random seeds.  Only relatively high frequency well localized binocular vectors are selected

Disparity Tuning Curves  Each patch is shown to both the eyes to get the tuning curve and the mean is considered as final curve.  These curves are defined in two parts: Tuned excitatory Tuned inhibitory  Tuned excitatory shows a strong peak at zero.  Tuned inhibitory shows opposite polarity.  Near unit’s right receptive slightly shifted giving positive preferred disparity.  Far unit has opposite positional offset with negative disparities.

Conclusion  ICA could be applied in denoising, compression or pattern recognition of color or stereo data.  ICA can be used to model computational properties of visual cortex (V1) cell.  Limitation: Since ICA emulate the behavior of cones it may fail in dark or un-illuminated images. To get better correlation basis patch needed to be small which may vary. Nonlinearities inherent in the conversion from RGB to cones response will affect the ICA result.